Electric Fields and Electric Potential

A charge creates a disturbance in the space around it that influences other charges. Rather than thinking of charges reaching out and touching one another at a distance, physicists describe this influence using the concept of a field. The electric field at a point is defined as the force per unit positive charge that a small test charge would experience if placed there:

$$E = \frac{F}{q}$$

The field $E$ is a vector, measured in newtons per coulomb ($\text{N C}^{-1}$) or equivalently volts per meter ($\text{V m}^{-1}$). Its direction is the direction of the force on a positive test charge. Because the test charge itself would create a field, we imagine it to be vanishingly small so that it does not disturb the field being measured.

For a single point charge $Q$, the field magnitude at dista